STATISTICAL-MECHANICS OF FRAGMENTATION PROCESSES OF ICE AND ROCK BODIES

It is a well-known experimental fact that impact fragmentation, specif ically of ice and rock bodies, causes a two-step (''knee''-shaped) pow er distribution of fragment masses with exponent values within the lim its -4 and -1.5 (here and henceforth the differential distribution is borne in mind). A new theoretical approach is proposed to determine th e exponent values, a minimal fracture mass, and properities of the kne e. As a basis for construction of nonequilibrium statistical mechanics of condensed matter fragmentation the maximum-entropy variational pri nciple is used. In contrast to the usual approach founded on the Boltz mann entropy the more general Tsallis entropy allowing stationary solu tions not only in the exponential Boltzmann-Gibbs form but in the form of the power (fractal) law distribution as well is invoked. Relying o n the analysis of a lot of published experiments a parameter beta is i ntroduced to describe an inhomogeneous distribution of the impact ener gy over the target. It varies from 0 (for an utterly inhomogeneous dis tribution of the impact energy) to 1 (for a homogeneous distribution). The lower limit of fragment masses is defined as a characteristic fra gment mass for which the energy of fragment formation is minimal. This mass value depends crucially on the value of beta. It is shown that f or beta much less than 1 only small fragment can be formed, and the ma ximal permitted fragment (of mass m(1)) is the upper boundary of the f irst stage of the fracture process and the point where the knee takes place. The second stage may be realized after a homogeneous redistribu tion of the remainder of the impact energy over the remainder of the t arget (when beta --> 1). Here, the formation of great fragments is per mitted only and the smallest of them (of mass m(2)) determines a lower boundary of the second stage. Different forms of the knee can be obse rved depending on relations between m(1) and m(2). Copyright (C) 1996 Elsevier Science Ltd